**Graphs**

*Graphs are a way of representing a rule such as "y is the same as x", "y is equal to x squared" or "x is always equal to 3". Really, it is that simple: the line on a graph represents a rule. At a more advanced level a way of thinking about graphs is that if an equation cannot be solved uniquely the graph is a way of representing the infinity of possible solutions.*

**Graphs Introduction**

Graphs are, in general, a way of representing the infinite number of solutions to an unsolvable equation. Cool!

A graph shows pairs of values: **left-and-right** and **up-and-down** represent two different things.

To save time it makes sense to get used to **common graphs**.

**Straight Line Graphs**

A graph that is a straight line!

What Different Gradients Look Like (YouTube)

**Polynomial Graphs**

Curved graphs with a predictable pattern depending on the index/power.

Graphs of Odd and Even Powers of Polynomial (YouTube)

*More polynomial playlists on the way. Request them if you want them soon!*

**Other Common Graphs**

Some other common types of equation have predicable shapes.

**Graph Transformations**

Graph transformations are talked about in other sections of UPmaths. This is section just looks at this topic in a bit more detail.

Transformations of Graphs in Direction of x and y Axes (YouTube)

Order for Combining Transformations in Direction of x and y Axes (YouTube)

**Graph Practice**

It can be good to do quick-fire revision of all the common graph shapes.

**Graphs of Functions**

A function is a pattern or relationship. Sometimes we do not know the equation or it may not have an equation.

Typical questions about graphs like this involve "transformations".

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